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expense (n.)

also formerly expence, late 14c., "action of spending or giving away, a laying out or expending," also "funds provided for expenses, expense money; damage or loss from any cause," from Anglo-French expense, Old French espense "money provided for expenses," from Late Latin expensa "disbursement, outlay, expense," noun use of neuter plural past participle of Latin expendere "weigh out money, pay down," from ex "out, out of" (see ex-) + pendere "to hang, cause to hang; weigh; pay" (from PIE root *(s)pen- "to draw, stretch, spin"). For the financial sense of the Latin verb, see pound (n.1). 

Latin spensa also yielded Medieval Latin spe(n)sa, the sense of which specialized to "outlay for provisions," then "provisions, food" before it was borrowed into Old High German as spisa and became the root of German Speise "food," now mostly meaning prepared food, and speisen "to eat." Expense account is from 1872.

expense (v.)

"offset (an expenditure) against an income," 1909, from expense (n.). Related: Expensed; expensing.

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Definitions of expense
1
expense (n.)
amounts paid for goods and services that may be currently tax deductible (as opposed to capital expenditures);
Synonyms: disbursal / disbursement
expense (n.)
a detriment or sacrifice;
at the expense of
expense (n.)
money spent to perform work and usually reimbursed by an employer;
he kept a careful record of his expenses at the meeting
2
expense (v.)
reduce the estimated value of something;
Synonyms: write off / write down
From wordnet.princeton.edu